Despite their attractiveness, popular perception is that techniques for nonparametric function approximation do not scale to streaming data due to an intractable growth in the amount of storage they require. To solve this problem in a memory-affordable way, we propose an online technique based on functional stochastic gradient descent in tandem with supervised sparsification based on greedy function subspace projections. The method, called parsimonious online learning with kernels (POLK), provides a controllable tradeoff between its solution accuracy and the amount of memory it requires. We derive conditions under which the generated function sequence converges almost surely to the optimal function, and we establish that the memory requirement remains finite. We evaluate POLK for kernel multi-class logistic regression and kernel hinge-loss classification on three canonical data sets: a synthetic Gaussian mixture model, the MNIST hand-written digits, and the Brodatz texture database. On all three tasks, we observe a favorable trade-off of objective function evaluation, classification performance, and complexity of the nonparametric regressor extracted the proposed method.

We develop a framework for controlling a team of robots to maintain and improve a communication bridge between a stationary robot and an independently exploring robot in a walled environment. We make use of two metrics for characterizing the communication: the Fiedler value of the weighted Laplacian describing the communication interactions of all the robots in the system, and the k-connectivity matrix that expresses which robots can interact through k or less intermediary robots. At each step, we move in such a way as to improve the Fiedler value as much as possible while keeping the number of intermediary robots between the two robots of interest below a desired value. We demonstrate the use of this framework in a scenario where the hop-count constraint cannot be satisfied, but show that communication quality is maintained anyways.

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This paper develops analytical techniques to delineate the workspace boundaries for parallel mechanisms with cables. In such mechanisms, it is not only necessary to solve the closure equations but it is also essential to verify that equilibrium can be achieved with non-negative actuator (cable) forces. We use tools from convex analysis and linear algebra to derive closed-form expressions for the workspace boundaries and illustrate the applications using planar and spatial examples.